Derivative Riemann solvers for systems of conservation laws and ADER methods

被引：157

作者：

Toro, EF

Titarev, VA ^{[1
]}

机构：

[1] Univ Trent, Dept Math, Fac Sci, I-38050 Trento, Italy

[2] Univ Trent, Fac Engn, Lab Appl Math, Trento, Italy

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2006年 / 212卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

hyperbolic systems; derivative Riemann problem; piece-wise smooth data; evolved-data Riemann solvers; arbitrary-order schemes; ADER method;

D O I：

10.1016/j.jcp.2005.06.018

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we first briefly review the semi-analytical method [E.F. Toro, V.A. Titarev, Solution of the generalized Riemann problem for advection-reaction equations, Proc. Roy. Soc. London 458 (2018) (2002) 271-281] for solving the derivative Riemann problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection schemes. We provide numerical examples for the compressible Euler equations in two space dimensions which illustrate robustness and high accuracy of the resulting schemes. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：150 / 165

页数：16

共 26 条

[1] A 2ND-ORDER GODUNOV-TYPE SCHEME FOR COMPRESSIBLE FLUID-DYNAMICS [J].